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arXiv · 2406.01856

On Approximation of Robust Max-Cut and Related Problems using Randomized Rounding Algorithms

Haoyan Shi·Sanjay Mehrotra
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Abstract

Goemans and Williamson proposed a randomized rounding algorithm for the MAX-CUT problem with a 0.878 approximation bound in expectation. The 0.878 approximation bound remains the best-known approximation bound for this APX-hard problem. Their approach was subsequently applied to other related problems such as Max-DiCut, MAX-SAT, and Max-2SAT, etc. We show that the randomized rounding algorithm can also be used to achieve a 0.878 approximation bound for the robust and distributionally robust counterparts of the max-cut problem. We also show that the approximation bounds for the other problems are maintained for their robust and distributionally robust counterparts if the randomization projection framework is used.

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Haoyan Shi, Sanjay Mehrotra. 2024-06-04. On Approximation of Robust Max-Cut and Related Problems using Randomized Rounding Algorithms. https://arxiv.org/abs/2406.01856

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